Editing Tuple (section)

{{short description|Finite ordered list of elements}}
{{hatnote group|{{for|the musical term|Tuplet}}{{redirect|Octuple|the boat|Octuple scull}}{{redirect|Duodecuple|the musical technique|Twelve-tone technique}}{{redirect|Sextuple|the sporting achievement of association football|Sextuple (association football)}}
}}

In [[mathematics]], a '''tuple''' is a finite [[sequence]] or ''ordered list'' of [[number]]s or, more generally, [[mathematical object]]s, which are called the ''elements'' of the tuple. An '''{{mvar|n}}-tuple''' is a tuple of {{mvar|n}} elements, where {{mvar|n}} is a non-negative [[integer]]. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a [[singleton (mathematics)|singleton]] and an [[ordered pair]], respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''.

Tuples are usually written by listing the elements within parentheses "{{math|( )}}" and separated by commas; for example, {{math|(2, 7, 4, 1, 7)}} denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning.{{efn|[[Square bracket]]s are used for [[matrix (mathematics)|matrices]], including [[row vector]]s. [[Braces (punctuation)|Braces]] are used for [[set (mathematics)|set]]s. Each [[programming language]] has its own convention for the different brackets.}}

An {{mvar|n}}-tuple can be formally defined as the [[image (function)|image]] of a [[function (mathematics)|function]] that has the set of the {{mvar|n}} first [[natural number]]s as its [[domain of a function|domain]]. Tuples may be also defined from ordered pairs by a [[recurrence relation|recurrence]] starting from an [[ordered pair]]; indeed, an {{mvar|n}}-tuple can be identified with the ordered pair of its {{math|(''n'' − 1)}} first elements and its {{mvar|n}}th element, for example, <math>
\left( \left( \left( 1,2 \right),3 \right),4 \right)=\left( 1,2,3,4 \right)</math>.

In [[computer science]], tuples come in many forms. Most typed [[functional programming]] languages implement tuples directly as [[product type]]s,<ref>{{cite web|url=https://wiki.haskell.org/Algebraic_data_type|title=Algebraic data type - HaskellWiki|website=wiki.haskell.org}}</ref> tightly associated with [[algebraic data type]]s, [[pattern matching]], and [[Assignment (computer science)#Parallel assignment|destructuring assignment]].<ref>{{cite web|url=https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Destructuring_assignment|title=Destructuring assignment|website=MDN Web Docs|date=18 April 2023 }}</ref> Many programming languages offer an alternative to tuples, known as [[Record (computer science)|record types]], featuring unordered elements accessed by label.<ref>{{cite web|url=https://stackoverflow.com/q/5525795 |title=Does JavaScript Guarantee Object Property Order?|website=Stack Overflow}}</ref> A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in [[struct (C programming language)|C structs]] and Haskell records. [[Relational database]]s may formally identify their [[Row (database)|rows]] (records) as ''tuples''.

Tuples also occur in [[relational algebra]]; when programming the [[semantic web]] with the [[Resource Description Framework]] (RDF); in [[linguistics]];<ref>{{cite encyclopedia|url= http://www.oxfordreference.com/view/10.1093/acref/9780199202720.001.0001/acref-9780199202720-e-2276|title= N-tuple|encyclopedia=The Concise Oxford Dictionary of Linguistics|date= January 2007|publisher= Oxford University Press|isbn= 9780199202720|editor-first=P. H.|editor-last=Matthews|access-date= 1 May 2015}}</ref> and in [[philosophy]].<ref>
{{cite book
| last1 = Blackburn
| first1 = Simon
| author-link1 = Simon Blackburn
| year = 1994
| chapter = ordered n-tuple
| title = The Oxford Dictionary of Philosophy
| url = https://books.google.com/books?id=Mno8CwAAQBAJ
| edition = 3
| location = Oxford
| publisher = Oxford University Press
| publication-date = 2016
| page = 342
| series = Oxford guidelines quick reference
| isbn = 9780198735304
| access-date = 2017-06-30
| quote = ordered n-tuple[:] A generalization of the notion of an [...] ordered pair to sequences of n objects.
}}
</ref>